1st thing to do is replace the oil sending unit, they can go bad. Mine did this a couple years ago, replaced it with a new part from Autozone and it has never done it again....
If it still does it with a new sending unit, then you need to hook up a gauge and check actual oil pressure or read it with an advanced scanner....

I would not drive it till you have this resolved; low oil pressure can be catastrophic!!!

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Supporting Vendor and Moderator of LOST05 Jeep Liberty CRD Limited 
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2mic.Sec.Fuel Filter
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